url stringclasses 147 values | commit stringclasses 147 values | file_path stringlengths 7 101 | full_name stringlengths 1 94 | start stringlengths 6 10 | end stringlengths 6 11 | tactic stringlengths 1 11.2k | state_before stringlengths 3 2.09M | state_after stringlengths 6 2.09M | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_push_colors | [83, 1] | [115, 12] | omega | f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
e0 : k ≠ d.size
e1 : k ≠ d.size + 1
e2 : k ≠ d.size + 2
e3 : k ≠ d.size + 3
lt0 : k < d.size
lt1 : k < d.size + 1
lt2 : k < d.size + 2
lt3 : k < d.size + 3
⊢ k < d.size + 4 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
e0 : k ≠ d.size
e1 : k ≠ d.size + 1
e2 : k ≠ d.size + 2
e3 : k ≠ d.size + 3
lt0 : k < d.size
lt1 : k < d.size + 1
lt2 : k < d.size + 2
lt3 : k < d.size + 3
⊢ k < d.size + 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_push_colors | [83, 1] | [115, 12] | have ge : d.size + 4 ≤ k := by omega | case neg
f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
e0 : k ≠ d.size
e1 : k ≠ d.size + 1
e2 : k ≠ d.size + 2
e3 : k ≠ d.size + 3
lt0 : ¬k < d.size
⊢ (if k < d.size + 4 then
if k < d.size + 3 then
if k < d.size + 2 then
if k < d.size + 1 then if k < d.size then d.get! k else if k = d.size then (f o).r else default
else if k = d.size + 1 then (f o).g else default
else if k = d.size + 2 then (f o).b else default
else if k = d.size + 3 then (f o).a else default
else (f (o + (1 + (k - (d.size + 4)) / 4)))[↑(k - (d.size + 4))]) =
if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)] | case neg
f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
e0 : k ≠ d.size
e1 : k ≠ d.size + 1
e2 : k ≠ d.size + 2
e3 : k ≠ d.size + 3
lt0 : ¬k < d.size
ge : d.size + 4 ≤ k
⊢ (if k < d.size + 4 then
if k < d.size + 3 then
if k < d.size + 2 then
if k < d.size + 1 then if k < d.size then d.get! k else if k = d.size then (f o).r else default
else if k = d.size + 1 then (f o).g else default
else if k = d.size + 2 then (f o).b else default
else if k = d.size + 3 then (f o).a else default
else (f (o + (1 + (k - (d.size + 4)) / 4)))[↑(k - (d.size + 4))]) =
if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)] | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
e0 : k ≠ d.size
e1 : k ≠ d.size + 1
e2 : k ≠ d.size + 2
e3 : k ≠ d.size + 3
lt0 : ¬k < d.size
⊢ (if k < d.size + 4 then
if k < d.size + 3 then
if k < d.size + 2 then
if k < d.size + 1 then if k < d.size then d.get! k else if k = d.size then (f o).r else default
else if k = d.size + 1 then (f o).g else default
else if k = d.size + 2 then (f o).b else default
else if k = d.size + 3 then (f o).a else default
else (f (o + (1 + (k - (d.size + 4)) / 4)))[↑(k - (d.size + 4))]) =
if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_push_colors | [83, 1] | [115, 12] | have e0 : o + (1 + (k - (d.size + 4)) / 4) = o + (k - d.size) / 4 := by omega | case neg
f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
e0 : k ≠ d.size
e1 : k ≠ d.size + 1
e2 : k ≠ d.size + 2
e3 : k ≠ d.size + 3
lt0 : ¬k < d.size
ge : d.size + 4 ≤ k
⊢ (if k < d.size + 4 then
if k < d.size + 3 then
if k < d.size + 2 then
if k < d.size + 1 then if k < d.size then d.get! k else if k = d.size then (f o).r else default
else if k = d.size + 1 then (f o).g else default
else if k = d.size + 2 then (f o).b else default
else if k = d.size + 3 then (f o).a else default
else (f (o + (1 + (k - (d.size + 4)) / 4)))[↑(k - (d.size + 4))]) =
if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)] | case neg
f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
e0✝ : k ≠ d.size
e1 : k ≠ d.size + 1
e2 : k ≠ d.size + 2
e3 : k ≠ d.size + 3
lt0 : ¬k < d.size
ge : d.size + 4 ≤ k
e0 : o + (1 + (k - (d.size + 4)) / 4) = o + (k - d.size) / 4
⊢ (if k < d.size + 4 then
if k < d.size + 3 then
if k < d.size + 2 then
if k < d.size + 1 then if k < d.size then d.get! k else if k = d.size then (f o).r else default
else if k = d.size + 1 then (f o).g else default
else if k = d.size + 2 then (f o).b else default
else if k = d.size + 3 then (f o).a else default
else (f (o + (1 + (k - (d.size + 4)) / 4)))[↑(k - (d.size + 4))]) =
if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)] | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
e0 : k ≠ d.size
e1 : k ≠ d.size + 1
e2 : k ≠ d.size + 2
e3 : k ≠ d.size + 3
lt0 : ¬k < d.size
ge : d.size + 4 ≤ k
⊢ (if k < d.size + 4 then
if k < d.size + 3 then
if k < d.size + 2 then
if k < d.size + 1 then if k < d.size then d.get! k else if k = d.size then (f o).r else default
else if k = d.size + 1 then (f o).g else default
else if k = d.size + 2 then (f o).b else default
else if k = d.size + 3 then (f o).a else default
else (f (o + (1 + (k - (d.size + 4)) / 4)))[↑(k - (d.size + 4))]) =
if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_push_colors | [83, 1] | [115, 12] | have e1 : k - d.size = k - (d.size + 4) + 4 := by omega | case neg
f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
e0✝ : k ≠ d.size
e1 : k ≠ d.size + 1
e2 : k ≠ d.size + 2
e3 : k ≠ d.size + 3
lt0 : ¬k < d.size
ge : d.size + 4 ≤ k
e0 : o + (1 + (k - (d.size + 4)) / 4) = o + (k - d.size) / 4
⊢ (if k < d.size + 4 then
if k < d.size + 3 then
if k < d.size + 2 then
if k < d.size + 1 then if k < d.size then d.get! k else if k = d.size then (f o).r else default
else if k = d.size + 1 then (f o).g else default
else if k = d.size + 2 then (f o).b else default
else if k = d.size + 3 then (f o).a else default
else (f (o + (1 + (k - (d.size + 4)) / 4)))[↑(k - (d.size + 4))]) =
if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)] | case neg
f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
e0✝ : k ≠ d.size
e1✝ : k ≠ d.size + 1
e2 : k ≠ d.size + 2
e3 : k ≠ d.size + 3
lt0 : ¬k < d.size
ge : d.size + 4 ≤ k
e0 : o + (1 + (k - (d.size + 4)) / 4) = o + (k - d.size) / 4
e1 : k - d.size = k - (d.size + 4) + 4
⊢ (if k < d.size + 4 then
if k < d.size + 3 then
if k < d.size + 2 then
if k < d.size + 1 then if k < d.size then d.get! k else if k = d.size then (f o).r else default
else if k = d.size + 1 then (f o).g else default
else if k = d.size + 2 then (f o).b else default
else if k = d.size + 3 then (f o).a else default
else (f (o + (1 + (k - (d.size + 4)) / 4)))[↑(k - (d.size + 4))]) =
if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)] | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
e0✝ : k ≠ d.size
e1 : k ≠ d.size + 1
e2 : k ≠ d.size + 2
e3 : k ≠ d.size + 3
lt0 : ¬k < d.size
ge : d.size + 4 ≤ k
e0 : o + (1 + (k - (d.size + 4)) / 4) = o + (k - d.size) / 4
⊢ (if k < d.size + 4 then
if k < d.size + 3 then
if k < d.size + 2 then
if k < d.size + 1 then if k < d.size then d.get! k else if k = d.size then (f o).r else default
else if k = d.size + 1 then (f o).g else default
else if k = d.size + 2 then (f o).b else default
else if k = d.size + 3 then (f o).a else default
else (f (o + (1 + (k - (d.size + 4)) / 4)))[↑(k - (d.size + 4))]) =
if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_push_colors | [83, 1] | [115, 12] | simp only [not_lt.mpr ge, ↓reduceIte, Nat.succ_eq_add_one, e0, e1, lt0, Nat.cast_add,
Fin.natCast_self, add_zero] | case neg
f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
e0✝ : k ≠ d.size
e1✝ : k ≠ d.size + 1
e2 : k ≠ d.size + 2
e3 : k ≠ d.size + 3
lt0 : ¬k < d.size
ge : d.size + 4 ≤ k
e0 : o + (1 + (k - (d.size + 4)) / 4) = o + (k - d.size) / 4
e1 : k - d.size = k - (d.size + 4) + 4
⊢ (if k < d.size + 4 then
if k < d.size + 3 then
if k < d.size + 2 then
if k < d.size + 1 then if k < d.size then d.get! k else if k = d.size then (f o).r else default
else if k = d.size + 1 then (f o).g else default
else if k = d.size + 2 then (f o).b else default
else if k = d.size + 3 then (f o).a else default
else (f (o + (1 + (k - (d.size + 4)) / 4)))[↑(k - (d.size + 4))]) =
if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
e0✝ : k ≠ d.size
e1✝ : k ≠ d.size + 1
e2 : k ≠ d.size + 2
e3 : k ≠ d.size + 3
lt0 : ¬k < d.size
ge : d.size + 4 ≤ k
e0 : o + (1 + (k - (d.size + 4)) / 4) = o + (k - d.size) / 4
e1 : k - d.size = k - (d.size + 4) + 4
⊢ (if k < d.size + 4 then
if k < d.size + 3 then
if k < d.size + 2 then
if k < d.size + 1 then if k < d.size then d.get! k else if k = d.size then (f o).r else default
else if k = d.size + 1 then (f o).g else default
else if k = d.size + 2 then (f o).b else default
else if k = d.size + 3 then (f o).a else default
else (f (o + (1 + (k - (d.size + 4)) / 4)))[↑(k - (d.size + 4))]) =
if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_push_colors | [83, 1] | [115, 12] | omega | f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
e0 : k ≠ d.size
e1 : k ≠ d.size + 1
e2 : k ≠ d.size + 2
e3 : k ≠ d.size + 3
lt0 : ¬k < d.size
⊢ d.size + 4 ≤ k | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
e0 : k ≠ d.size
e1 : k ≠ d.size + 1
e2 : k ≠ d.size + 2
e3 : k ≠ d.size + 3
lt0 : ¬k < d.size
⊢ d.size + 4 ≤ k
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_push_colors | [83, 1] | [115, 12] | omega | f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
e0 : k ≠ d.size
e1 : k ≠ d.size + 1
e2 : k ≠ d.size + 2
e3 : k ≠ d.size + 3
lt0 : ¬k < d.size
ge : d.size + 4 ≤ k
⊢ o + (1 + (k - (d.size + 4)) / 4) = o + (k - d.size) / 4 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
e0 : k ≠ d.size
e1 : k ≠ d.size + 1
e2 : k ≠ d.size + 2
e3 : k ≠ d.size + 3
lt0 : ¬k < d.size
ge : d.size + 4 ≤ k
⊢ o + (1 + (k - (d.size + 4)) / 4) = o + (k - d.size) / 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_push_colors | [83, 1] | [115, 12] | omega | f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
e0✝ : k ≠ d.size
e1 : k ≠ d.size + 1
e2 : k ≠ d.size + 2
e3 : k ≠ d.size + 3
lt0 : ¬k < d.size
ge : d.size + 4 ≤ k
e0 : o + (1 + (k - (d.size + 4)) / 4) = o + (k - d.size) / 4
⊢ k - d.size = k - (d.size + 4) + 4 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
e0✝ : k ≠ d.size
e1 : k ≠ d.size + 1
e2 : k ≠ d.size + 2
e3 : k ≠ d.size + 3
lt0 : ¬k < d.size
ge : d.size + 4 ≤ k
e0 : o + (1 + (k - (d.size + 4)) / 4) = o + (k - d.size) / 4
⊢ k - d.size = k - (d.size + 4) + 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_push_colors | [83, 1] | [115, 12] | simp only [ByteArray.size_push] | case succ.lt
f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
⊢ k < ((((d.push (f o).r).push (f o).g).push (f o).b).push (f o).a).size + n * 4 | case succ.lt
f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
⊢ k < d.size + 1 + 1 + 1 + 1 + n * 4 | Please generate a tactic in lean4 to solve the state.
STATE:
case succ.lt
f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
⊢ k < ((((d.push (f o).r).push (f o).g).push (f o).b).push (f o).a).size + n * 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_push_colors | [83, 1] | [115, 12] | omega | case succ.lt
f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
⊢ k < d.size + 1 + 1 + 1 + 1 + n * 4 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case succ.lt
f : ℕ → Color UInt8
k n : ℕ
h :
∀ (o : ℕ) (d : ByteArray),
k < d.size + n * 4 →
(push_colors f n o d).get! k = if k < d.size then d.get! k else (f (o + (k - d.size) / 4))[↑(k - d.size)]
o : ℕ
d : ByteArray
lt : k < d.size + n * 4 + 4
⊢ k < d.size + 1 + 1 + 1 + 1 + n * 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_push_colors | [117, 1] | [123, 71] | simp only [getElem_fin, ByteArray.getElemNat_eq_get!, dite_eq_ite] | f : ℕ → Color UInt8
n o : ℕ
d : ByteArray
k : Fin (push_colors f n o d).size
⊢ (push_colors f n o d)[k] = if h : ↑k < d.size then d[k] else (f (o + (↑k - d.size) / 4))[↑(↑k - d.size)] | f : ℕ → Color UInt8
n o : ℕ
d : ByteArray
k : Fin (push_colors f n o d).size
⊢ (push_colors f n o d).get! ↑k = if ↑k < d.size then d.get! ↑k else (f (o + (↑k - d.size) / 4))[↑(↑k - d.size)] | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → Color UInt8
n o : ℕ
d : ByteArray
k : Fin (push_colors f n o d).size
⊢ (push_colors f n o d)[k] = if h : ↑k < d.size then d[k] else (f (o + (↑k - d.size) / 4))[↑(↑k - d.size)]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_push_colors | [117, 1] | [123, 71] | apply get!_push_colors | f : ℕ → Color UInt8
n o : ℕ
d : ByteArray
k : Fin (push_colors f n o d).size
⊢ (push_colors f n o d).get! ↑k = if ↑k < d.size then d.get! ↑k else (f (o + (↑k - d.size) / 4))[↑(↑k - d.size)] | case lt
f : ℕ → Color UInt8
n o : ℕ
d : ByteArray
k : Fin (push_colors f n o d).size
⊢ ↑k < d.size + n * 4 | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → Color UInt8
n o : ℕ
d : ByteArray
k : Fin (push_colors f n o d).size
⊢ (push_colors f n o d).get! ↑k = if ↑k < d.size then d.get! ↑k else (f (o + (↑k - d.size) / 4))[↑(↑k - d.size)]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_push_colors | [117, 1] | [123, 71] | convert k.prop | case lt
f : ℕ → Color UInt8
n o : ℕ
d : ByteArray
k : Fin (push_colors f n o d).size
⊢ ↑k < d.size + n * 4 | case h.e'_4
f : ℕ → Color UInt8
n o : ℕ
d : ByteArray
k : Fin (push_colors f n o d).size
⊢ d.size + n * 4 = (push_colors f n o d).size | Please generate a tactic in lean4 to solve the state.
STATE:
case lt
f : ℕ → Color UInt8
n o : ℕ
d : ByteArray
k : Fin (push_colors f n o d).size
⊢ ↑k < d.size + n * 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_push_colors | [117, 1] | [123, 71] | simp only [size_push_colors] | case h.e'_4
f : ℕ → Color UInt8
n o : ℕ
d : ByteArray
k : Fin (push_colors f n o d).size
⊢ d.size + n * 4 = (push_colors f n o d).size | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_4
f : ℕ → Color UInt8
n o : ℕ
d : ByteArray
k : Fin (push_colors f n o d).size
⊢ d.size + n * 4 = (push_colors f n o d).size
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.n0_lt_n | [130, 1] | [131, 37] | simp only [le_max_iff] at h | n chunk : ℕ
h : ¬n ≤ max 1 chunk
⊢ n / 2 < n | n chunk : ℕ
h : ¬(n ≤ 1 ∨ n ≤ chunk)
⊢ n / 2 < n | Please generate a tactic in lean4 to solve the state.
STATE:
n chunk : ℕ
h : ¬n ≤ max 1 chunk
⊢ n / 2 < n
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.n0_lt_n | [130, 1] | [131, 37] | omega | n chunk : ℕ
h : ¬(n ≤ 1 ∨ n ≤ chunk)
⊢ n / 2 < n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n chunk : ℕ
h : ¬(n ≤ 1 ∨ n ≤ chunk)
⊢ n / 2 < n
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.n1_lt_n | [132, 1] | [133, 37] | simp only [le_max_iff] at h | n chunk : ℕ
h : ¬n ≤ max 1 chunk
⊢ n - n / 2 < n | n chunk : ℕ
h : ¬(n ≤ 1 ∨ n ≤ chunk)
⊢ n - n / 2 < n | Please generate a tactic in lean4 to solve the state.
STATE:
n chunk : ℕ
h : ¬n ≤ max 1 chunk
⊢ n - n / 2 < n
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.n1_lt_n | [132, 1] | [133, 37] | omega | n chunk : ℕ
h : ¬(n ≤ 1 ∨ n ≤ chunk)
⊢ n - n / 2 < n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n chunk : ℕ
h : ¬(n ≤ 1 ∨ n ≤ chunk)
⊢ n - n / 2 < n
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.size_parallel_colors' | [152, 1] | [160, 10] | induction' n using Nat.strong_induction_on with n i generalizing o | f : ℕ → Color UInt8
n o chunk : ℕ
⊢ (parallel_colors' f n o chunk).size = n * 4 | case h
f : ℕ → Color UInt8
chunk n : ℕ
i : ∀ m < n, ∀ (o : ℕ), (parallel_colors' f m o chunk).size = m * 4
o : ℕ
⊢ (parallel_colors' f n o chunk).size = n * 4 | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → Color UInt8
n o chunk : ℕ
⊢ (parallel_colors' f n o chunk).size = n * 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.size_parallel_colors' | [152, 1] | [160, 10] | rw [parallel_colors'] | case h
f : ℕ → Color UInt8
chunk n : ℕ
i : ∀ m < n, ∀ (o : ℕ), (parallel_colors' f m o chunk).size = m * 4
o : ℕ
⊢ (parallel_colors' f n o chunk).size = n * 4 | case h
f : ℕ → Color UInt8
chunk n : ℕ
i : ∀ m < n, ∀ (o : ℕ), (parallel_colors' f m o chunk).size = m * 4
o : ℕ
⊢ (if n ≤ max 1 chunk then push_colors f n o (ByteArray.mkEmpty n)
else
let n0 := n / 2;
let t0 := Task.spawn fun x => parallel_colors' f n0 o chunk;
let t1 := Task.spawn fun x => parallel_colors' f (n - n0) (o + n0) chunk;
t0.get ++ t1.get).size =
n * 4 | Please generate a tactic in lean4 to solve the state.
STATE:
case h
f : ℕ → Color UInt8
chunk n : ℕ
i : ∀ m < n, ∀ (o : ℕ), (parallel_colors' f m o chunk).size = m * 4
o : ℕ
⊢ (parallel_colors' f n o chunk).size = n * 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.size_parallel_colors' | [152, 1] | [160, 10] | by_cases h : n ≤ max 1 chunk | case h
f : ℕ → Color UInt8
chunk n : ℕ
i : ∀ m < n, ∀ (o : ℕ), (parallel_colors' f m o chunk).size = m * 4
o : ℕ
⊢ (if n ≤ max 1 chunk then push_colors f n o (ByteArray.mkEmpty n)
else
let n0 := n / 2;
let t0 := Task.spawn fun x => parallel_colors' f n0 o chunk;
let t1 := Task.spawn fun x => parallel_colors' f (n - n0) (o + n0) chunk;
t0.get ++ t1.get).size =
n * 4 | case pos
f : ℕ → Color UInt8
chunk n : ℕ
i : ∀ m < n, ∀ (o : ℕ), (parallel_colors' f m o chunk).size = m * 4
o : ℕ
h : n ≤ max 1 chunk
⊢ (if n ≤ max 1 chunk then push_colors f n o (ByteArray.mkEmpty n)
else
let n0 := n / 2;
let t0 := Task.spawn fun x => parallel_colors' f n0 o chunk;
let t1 := Task.spawn fun x => parallel_colors' f (n - n0) (o + n0) chunk;
t0.get ++ t1.get).size =
n * 4
case neg
f : ℕ → Color UInt8
chunk n : ℕ
i : ∀ m < n, ∀ (o : ℕ), (parallel_colors' f m o chunk).size = m * 4
o : ℕ
h : ¬n ≤ max 1 chunk
⊢ (if n ≤ max 1 chunk then push_colors f n o (ByteArray.mkEmpty n)
else
let n0 := n / 2;
let t0 := Task.spawn fun x => parallel_colors' f n0 o chunk;
let t1 := Task.spawn fun x => parallel_colors' f (n - n0) (o + n0) chunk;
t0.get ++ t1.get).size =
n * 4 | Please generate a tactic in lean4 to solve the state.
STATE:
case h
f : ℕ → Color UInt8
chunk n : ℕ
i : ∀ m < n, ∀ (o : ℕ), (parallel_colors' f m o chunk).size = m * 4
o : ℕ
⊢ (if n ≤ max 1 chunk then push_colors f n o (ByteArray.mkEmpty n)
else
let n0 := n / 2;
let t0 := Task.spawn fun x => parallel_colors' f n0 o chunk;
let t1 := Task.spawn fun x => parallel_colors' f (n - n0) (o + n0) chunk;
t0.get ++ t1.get).size =
n * 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.size_parallel_colors' | [152, 1] | [160, 10] | simp only [h, if_true, size_push_colors, ByteArray.size_mkEmpty, zero_add] | case pos
f : ℕ → Color UInt8
chunk n : ℕ
i : ∀ m < n, ∀ (o : ℕ), (parallel_colors' f m o chunk).size = m * 4
o : ℕ
h : n ≤ max 1 chunk
⊢ (if n ≤ max 1 chunk then push_colors f n o (ByteArray.mkEmpty n)
else
let n0 := n / 2;
let t0 := Task.spawn fun x => parallel_colors' f n0 o chunk;
let t1 := Task.spawn fun x => parallel_colors' f (n - n0) (o + n0) chunk;
t0.get ++ t1.get).size =
n * 4 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
f : ℕ → Color UInt8
chunk n : ℕ
i : ∀ m < n, ∀ (o : ℕ), (parallel_colors' f m o chunk).size = m * 4
o : ℕ
h : n ≤ max 1 chunk
⊢ (if n ≤ max 1 chunk then push_colors f n o (ByteArray.mkEmpty n)
else
let n0 := n / 2;
let t0 := Task.spawn fun x => parallel_colors' f n0 o chunk;
let t1 := Task.spawn fun x => parallel_colors' f (n - n0) (o + n0) chunk;
t0.get ++ t1.get).size =
n * 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.size_parallel_colors' | [152, 1] | [160, 10] | simp only [h, if_false, Task.spawn, ByteArray.size_append, i _ (n0_lt_n h), i _ (n1_lt_n h)] | case neg
f : ℕ → Color UInt8
chunk n : ℕ
i : ∀ m < n, ∀ (o : ℕ), (parallel_colors' f m o chunk).size = m * 4
o : ℕ
h : ¬n ≤ max 1 chunk
⊢ (if n ≤ max 1 chunk then push_colors f n o (ByteArray.mkEmpty n)
else
let n0 := n / 2;
let t0 := Task.spawn fun x => parallel_colors' f n0 o chunk;
let t1 := Task.spawn fun x => parallel_colors' f (n - n0) (o + n0) chunk;
t0.get ++ t1.get).size =
n * 4 | case neg
f : ℕ → Color UInt8
chunk n : ℕ
i : ∀ m < n, ∀ (o : ℕ), (parallel_colors' f m o chunk).size = m * 4
o : ℕ
h : ¬n ≤ max 1 chunk
⊢ n / 2 * 4 + (n - n / 2) * 4 = n * 4 | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
f : ℕ → Color UInt8
chunk n : ℕ
i : ∀ m < n, ∀ (o : ℕ), (parallel_colors' f m o chunk).size = m * 4
o : ℕ
h : ¬n ≤ max 1 chunk
⊢ (if n ≤ max 1 chunk then push_colors f n o (ByteArray.mkEmpty n)
else
let n0 := n / 2;
let t0 := Task.spawn fun x => parallel_colors' f n0 o chunk;
let t1 := Task.spawn fun x => parallel_colors' f (n - n0) (o + n0) chunk;
t0.get ++ t1.get).size =
n * 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.size_parallel_colors' | [152, 1] | [160, 10] | omega | case neg
f : ℕ → Color UInt8
chunk n : ℕ
i : ∀ m < n, ∀ (o : ℕ), (parallel_colors' f m o chunk).size = m * 4
o : ℕ
h : ¬n ≤ max 1 chunk
⊢ n / 2 * 4 + (n - n / 2) * 4 = n * 4 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
f : ℕ → Color UInt8
chunk n : ℕ
i : ∀ m < n, ∀ (o : ℕ), (parallel_colors' f m o chunk).size = m * 4
o : ℕ
h : ¬n ≤ max 1 chunk
⊢ n / 2 * 4 + (n - n / 2) * 4 = n * 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | have four : ((4 : ℕ) : Fin 4) = 0 := by decide | f : ℕ → Color UInt8
n o chunk k : ℕ
lt : k < n * 4
⊢ (parallel_colors' f n o chunk).get! k = (f (o + k / 4))[↑k] | f : ℕ → Color UInt8
n o chunk k : ℕ
lt : k < n * 4
four : ↑4 = 0
⊢ (parallel_colors' f n o chunk).get! k = (f (o + k / 4))[↑k] | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → Color UInt8
n o chunk k : ℕ
lt : k < n * 4
⊢ (parallel_colors' f n o chunk).get! k = (f (o + k / 4))[↑k]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | induction' n using Nat.strong_induction_on with n i generalizing o k | f : ℕ → Color UInt8
n o chunk k : ℕ
lt : k < n * 4
four : ↑4 = 0
⊢ (parallel_colors' f n o chunk).get! k = (f (o + k / 4))[↑k] | case h
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
⊢ (parallel_colors' f n o chunk).get! k = (f (o + k / 4))[↑k] | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → Color UInt8
n o chunk k : ℕ
lt : k < n * 4
four : ↑4 = 0
⊢ (parallel_colors' f n o chunk).get! k = (f (o + k / 4))[↑k]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | rw [parallel_colors'] | case h
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
⊢ (parallel_colors' f n o chunk).get! k = (f (o + k / 4))[↑k] | case h
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
⊢ (if n ≤ max 1 chunk then push_colors f n o (ByteArray.mkEmpty n)
else
let n0 := n / 2;
let t0 := Task.spawn fun x => parallel_colors' f n0 o chunk;
let t1 := Task.spawn fun x => parallel_colors' f (n - n0) (o + n0) chunk;
t0.get ++ t1.get).get!
k =
(f (o + k / 4))[↑k] | Please generate a tactic in lean4 to solve the state.
STATE:
case h
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
⊢ (parallel_colors' f n o chunk).get! k = (f (o + k / 4))[↑k]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | by_cases h : n ≤ max 1 chunk | case h
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
⊢ (if n ≤ max 1 chunk then push_colors f n o (ByteArray.mkEmpty n)
else
let n0 := n / 2;
let t0 := Task.spawn fun x => parallel_colors' f n0 o chunk;
let t1 := Task.spawn fun x => parallel_colors' f (n - n0) (o + n0) chunk;
t0.get ++ t1.get).get!
k =
(f (o + k / 4))[↑k] | case pos
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : n ≤ max 1 chunk
⊢ (if n ≤ max 1 chunk then push_colors f n o (ByteArray.mkEmpty n)
else
let n0 := n / 2;
let t0 := Task.spawn fun x => parallel_colors' f n0 o chunk;
let t1 := Task.spawn fun x => parallel_colors' f (n - n0) (o + n0) chunk;
t0.get ++ t1.get).get!
k =
(f (o + k / 4))[↑k]
case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : ¬n ≤ max 1 chunk
⊢ (if n ≤ max 1 chunk then push_colors f n o (ByteArray.mkEmpty n)
else
let n0 := n / 2;
let t0 := Task.spawn fun x => parallel_colors' f n0 o chunk;
let t1 := Task.spawn fun x => parallel_colors' f (n - n0) (o + n0) chunk;
t0.get ++ t1.get).get!
k =
(f (o + k / 4))[↑k] | Please generate a tactic in lean4 to solve the state.
STATE:
case h
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
⊢ (if n ≤ max 1 chunk then push_colors f n o (ByteArray.mkEmpty n)
else
let n0 := n / 2;
let t0 := Task.spawn fun x => parallel_colors' f n0 o chunk;
let t1 := Task.spawn fun x => parallel_colors' f (n - n0) (o + n0) chunk;
t0.get ++ t1.get).get!
k =
(f (o + k / 4))[↑k]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | decide | f : ℕ → Color UInt8
n o chunk k : ℕ
lt : k < n * 4
⊢ ↑4 = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → Color UInt8
n o chunk k : ℕ
lt : k < n * 4
⊢ ↑4 = 0
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | simp only [h, if_true, Task.spawn] | case pos
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : n ≤ max 1 chunk
⊢ (if n ≤ max 1 chunk then push_colors f n o (ByteArray.mkEmpty n)
else
let n0 := n / 2;
let t0 := Task.spawn fun x => parallel_colors' f n0 o chunk;
let t1 := Task.spawn fun x => parallel_colors' f (n - n0) (o + n0) chunk;
t0.get ++ t1.get).get!
k =
(f (o + k / 4))[↑k] | case pos
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : n ≤ max 1 chunk
⊢ (push_colors f n o (ByteArray.mkEmpty n)).get! k = (f (o + k / 4))[↑k] | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : n ≤ max 1 chunk
⊢ (if n ≤ max 1 chunk then push_colors f n o (ByteArray.mkEmpty n)
else
let n0 := n / 2;
let t0 := Task.spawn fun x => parallel_colors' f n0 o chunk;
let t1 := Task.spawn fun x => parallel_colors' f (n - n0) (o + n0) chunk;
t0.get ++ t1.get).get!
k =
(f (o + k / 4))[↑k]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | rw [get!_push_colors] | case pos
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : n ≤ max 1 chunk
⊢ (push_colors f n o (ByteArray.mkEmpty n)).get! k = (f (o + k / 4))[↑k] | case pos
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : n ≤ max 1 chunk
⊢ (if k < (ByteArray.mkEmpty n).size then (ByteArray.mkEmpty n).get! k
else (f (o + (k - (ByteArray.mkEmpty n).size) / 4))[↑(k - (ByteArray.mkEmpty n).size)]) =
(f (o + k / 4))[↑k]
case pos.lt
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : n ≤ max 1 chunk
⊢ k < (ByteArray.mkEmpty n).size + n * 4 | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : n ≤ max 1 chunk
⊢ (push_colors f n o (ByteArray.mkEmpty n)).get! k = (f (o + k / 4))[↑k]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | simp only [ByteArray.size_mkEmpty, not_lt_zero', ↓reduceIte, tsub_zero] | case pos
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : n ≤ max 1 chunk
⊢ (if k < (ByteArray.mkEmpty n).size then (ByteArray.mkEmpty n).get! k
else (f (o + (k - (ByteArray.mkEmpty n).size) / 4))[↑(k - (ByteArray.mkEmpty n).size)]) =
(f (o + k / 4))[↑k] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : n ≤ max 1 chunk
⊢ (if k < (ByteArray.mkEmpty n).size then (ByteArray.mkEmpty n).get! k
else (f (o + (k - (ByteArray.mkEmpty n).size) / 4))[↑(k - (ByteArray.mkEmpty n).size)]) =
(f (o + k / 4))[↑k]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | simpa only [ByteArray.size_mkEmpty, zero_add] | case pos.lt
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : n ≤ max 1 chunk
⊢ k < (ByteArray.mkEmpty n).size + n * 4 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.lt
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : n ≤ max 1 chunk
⊢ k < (ByteArray.mkEmpty n).size + n * 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | simp only [h, if_false, Task.spawn, ByteArray.get!_append, size_parallel_colors'] | case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : ¬n ≤ max 1 chunk
⊢ (if n ≤ max 1 chunk then push_colors f n o (ByteArray.mkEmpty n)
else
let n0 := n / 2;
let t0 := Task.spawn fun x => parallel_colors' f n0 o chunk;
let t1 := Task.spawn fun x => parallel_colors' f (n - n0) (o + n0) chunk;
t0.get ++ t1.get).get!
k =
(f (o + k / 4))[↑k] | case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : ¬n ≤ max 1 chunk
⊢ (if k < n / 2 * 4 then (parallel_colors' f (n / 2) o chunk).get! k
else (parallel_colors' f (n - n / 2) (o + n / 2) chunk).get! (k - n / 2 * 4)) =
(f (o + k / 4))[↑k] | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : ¬n ≤ max 1 chunk
⊢ (if n ≤ max 1 chunk then push_colors f n o (ByteArray.mkEmpty n)
else
let n0 := n / 2;
let t0 := Task.spawn fun x => parallel_colors' f n0 o chunk;
let t1 := Task.spawn fun x => parallel_colors' f (n - n0) (o + n0) chunk;
t0.get ++ t1.get).get!
k =
(f (o + k / 4))[↑k]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | simp only [le_max_iff, not_or, not_le] at h | case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : ¬n ≤ max 1 chunk
⊢ (if k < n / 2 * 4 then (parallel_colors' f (n / 2) o chunk).get! k
else (parallel_colors' f (n - n / 2) (o + n / 2) chunk).get! (k - n / 2 * 4)) =
(f (o + k / 4))[↑k] | case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
⊢ (if k < n / 2 * 4 then (parallel_colors' f (n / 2) o chunk).get! k
else (parallel_colors' f (n - n / 2) (o + n / 2) chunk).get! (k - n / 2 * 4)) =
(f (o + k / 4))[↑k] | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : ¬n ≤ max 1 chunk
⊢ (if k < n / 2 * 4 then (parallel_colors' f (n / 2) o chunk).get! k
else (parallel_colors' f (n - n / 2) (o + n / 2) chunk).get! (k - n / 2 * 4)) =
(f (o + k / 4))[↑k]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | by_cases c : k < n/2 * 4 | case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
⊢ (if k < n / 2 * 4 then (parallel_colors' f (n / 2) o chunk).get! k
else (parallel_colors' f (n - n / 2) (o + n / 2) chunk).get! (k - n / 2 * 4)) =
(f (o + k / 4))[↑k] | case pos
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : k < n / 2 * 4
⊢ (if k < n / 2 * 4 then (parallel_colors' f (n / 2) o chunk).get! k
else (parallel_colors' f (n - n / 2) (o + n / 2) chunk).get! (k - n / 2 * 4)) =
(f (o + k / 4))[↑k]
case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
⊢ (if k < n / 2 * 4 then (parallel_colors' f (n / 2) o chunk).get! k
else (parallel_colors' f (n - n / 2) (o + n / 2) chunk).get! (k - n / 2 * 4)) =
(f (o + k / 4))[↑k] | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
⊢ (if k < n / 2 * 4 then (parallel_colors' f (n / 2) o chunk).get! k
else (parallel_colors' f (n - n / 2) (o + n / 2) chunk).get! (k - n / 2 * 4)) =
(f (o + k / 4))[↑k]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | simp only [c, ↓reduceIte] | case pos
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : k < n / 2 * 4
⊢ (if k < n / 2 * 4 then (parallel_colors' f (n / 2) o chunk).get! k
else (parallel_colors' f (n - n / 2) (o + n / 2) chunk).get! (k - n / 2 * 4)) =
(f (o + k / 4))[↑k] | case pos
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : k < n / 2 * 4
⊢ (parallel_colors' f (n / 2) o chunk).get! k = (f (o + k / 4))[↑k] | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : k < n / 2 * 4
⊢ (if k < n / 2 * 4 then (parallel_colors' f (n / 2) o chunk).get! k
else (parallel_colors' f (n - n / 2) (o + n / 2) chunk).get! (k - n / 2 * 4)) =
(f (o + k / 4))[↑k]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | rw [i _ (by omega) _ _ (by omega)] | case pos
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : k < n / 2 * 4
⊢ (parallel_colors' f (n / 2) o chunk).get! k = (f (o + k / 4))[↑k] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : k < n / 2 * 4
⊢ (parallel_colors' f (n / 2) o chunk).get! k = (f (o + k / 4))[↑k]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | omega | f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : k < n / 2 * 4
⊢ n / 2 < n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : k < n / 2 * 4
⊢ n / 2 < n
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | omega | f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : k < n / 2 * 4
⊢ k < n / 2 * 4 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : k < n / 2 * 4
⊢ k < n / 2 * 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | simp only [c, ↓reduceIte] | case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
⊢ (if k < n / 2 * 4 then (parallel_colors' f (n / 2) o chunk).get! k
else (parallel_colors' f (n - n / 2) (o + n / 2) chunk).get! (k - n / 2 * 4)) =
(f (o + k / 4))[↑k] | case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
⊢ (parallel_colors' f (n - n / 2) (o + n / 2) chunk).get! (k - n / 2 * 4) = (f (o + k / 4))[↑k] | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
⊢ (if k < n / 2 * 4 then (parallel_colors' f (n / 2) o chunk).get! k
else (parallel_colors' f (n - n / 2) (o + n / 2) chunk).get! (k - n / 2 * 4)) =
(f (o + k / 4))[↑k]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | rw [i] | case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
⊢ (parallel_colors' f (n - n / 2) (o + n / 2) chunk).get! (k - n / 2 * 4) = (f (o + k / 4))[↑k] | case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
⊢ (f (o + n / 2 + (k - n / 2 * 4) / 4))[↑(k - n / 2 * 4)] = (f (o + k / 4))[↑k]
case neg.a
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
⊢ n - n / 2 < n
case neg.lt
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
⊢ k - n / 2 * 4 < (n - n / 2) * 4 | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
⊢ (parallel_colors' f (n - n / 2) (o + n / 2) chunk).get! (k - n / 2 * 4) = (f (o + k / 4))[↑k]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | have ke : o + n / 2 + (k - n / 2 * 4) / 4 = o + k / 4 := by omega | case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
⊢ (f (o + n / 2 + (k - n / 2 * 4) / 4))[↑(k - n / 2 * 4)] = (f (o + k / 4))[↑k] | case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
ke : o + n / 2 + (k - n / 2 * 4) / 4 = o + k / 4
⊢ (f (o + n / 2 + (k - n / 2 * 4) / 4))[↑(k - n / 2 * 4)] = (f (o + k / 4))[↑k] | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
⊢ (f (o + n / 2 + (k - n / 2 * 4) / 4))[↑(k - n / 2 * 4)] = (f (o + k / 4))[↑k]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | rw [Nat.cast_sub (by omega), Nat.cast_mul, four, mul_zero, sub_zero, ke] | case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
ke : o + n / 2 + (k - n / 2 * 4) / 4 = o + k / 4
⊢ (f (o + n / 2 + (k - n / 2 * 4) / 4))[↑(k - n / 2 * 4)] = (f (o + k / 4))[↑k] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
ke : o + n / 2 + (k - n / 2 * 4) / 4 = o + k / 4
⊢ (f (o + n / 2 + (k - n / 2 * 4) / 4))[↑(k - n / 2 * 4)] = (f (o + k / 4))[↑k]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | omega | f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
⊢ o + n / 2 + (k - n / 2 * 4) / 4 = o + k / 4 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
⊢ o + n / 2 + (k - n / 2 * 4) / 4 = o + k / 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | omega | f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
ke : o + n / 2 + (k - n / 2 * 4) / 4 = o + k / 4
⊢ n / 2 * 4 ≤ k | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
ke : o + n / 2 + (k - n / 2 * 4) / 4 = o + k / 4
⊢ n / 2 * 4 ≤ k
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | omega | case neg.a
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
⊢ n - n / 2 < n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
⊢ n - n / 2 < n
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors' | [162, 1] | [183, 14] | omega | case neg.lt
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
⊢ k - n / 2 * 4 < (n - n / 2) * 4 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.lt
f : ℕ → Color UInt8
chunk : ℕ
four : ↑4 = 0
n : ℕ
i : ∀ m < n, ∀ (o k : ℕ), k < m * 4 → (parallel_colors' f m o chunk).get! k = (f (o + k / 4))[↑k]
o k : ℕ
lt : k < n * 4
h : 1 < n ∧ chunk < n
c : ¬k < n / 2 * 4
⊢ k - n / 2 * 4 < (n - n / 2) * 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.size_parallel_colors | [185, 1] | [188, 53] | simp only [parallel_colors, size_parallel_colors'] | f : ℕ → Color UInt8
n chunk : ℕ
⊢ (parallel_colors f n chunk).size = n * 4 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → Color UInt8
n chunk : ℕ
⊢ (parallel_colors f n chunk).size = n * 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get!_parallel_colors | [190, 1] | [193, 80] | simp only [parallel_colors, zero_add, get!_parallel_colors' f n 0 chunk k lt] | f : ℕ → Color UInt8
n chunk k : ℕ
lt : k < n * 4
⊢ (parallel_colors f n chunk).get! k = (f (k / 4))[↑k] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → Color UInt8
n chunk k : ℕ
lt : k < n * 4
⊢ (parallel_colors f n chunk).get! k = (f (k / 4))[↑k]
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.width_ofFn | [204, 1] | [205, 49] | rw [ofFn] | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
⊢ (ofFn w h chunk f).width = w | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
⊢ (ofFn w h chunk f).width = w
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.height_ofFn | [206, 1] | [207, 50] | rw [ofFn] | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
⊢ (ofFn w h chunk f).height = h | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
⊢ (ofFn w h chunk f).height = h
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | rw [get] | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
⊢ (ofFn w h chunk f).get x y = f ↑x ↑y | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
⊢ (let b := base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y;
let_fun lt := ⋯;
{ r := (ofFn w h chunk f).data[b], g := (ofFn w h chunk f).data[b + 1], b := (ofFn w h chunk f).data[b + 2],
a := (ofFn w h chunk f).data[b + 3] }) =
f ↑x ↑y | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
⊢ (ofFn w h chunk f).get x y = f ↑x ↑y
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | simp only [ByteArray.getElemNat_eq_get!] | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
⊢ (let b := base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y;
let_fun lt := ⋯;
{ r := (ofFn w h chunk f).data[b], g := (ofFn w h chunk f).data[b + 1], b := (ofFn w h chunk f).data[b + 2],
a := (ofFn w h chunk f).data[b + 3] }) =
f ↑x ↑y | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
⊢ { r := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y),
g := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 1),
b := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 2),
a := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 3) } =
f ↑x ↑y | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
⊢ (let b := base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y;
let_fun lt := ⋯;
{ r := (ofFn w h chunk f).data[b], g := (ofFn w h chunk f).data[b + 1], b := (ofFn w h chunk f).data[b + 2],
a := (ofFn w h chunk f).data[b + 3] }) =
f ↑x ↑y
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | have xw := x.prop | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
⊢ { r := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y),
g := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 1),
b := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 2),
a := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 3) } =
f ↑x ↑y | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < (ofFn w h chunk f).width
⊢ { r := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y),
g := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 1),
b := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 2),
a := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 3) } =
f ↑x ↑y | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
⊢ { r := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y),
g := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 1),
b := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 2),
a := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 3) } =
f ↑x ↑y
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | have yh := y.prop | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < (ofFn w h chunk f).width
⊢ { r := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y),
g := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 1),
b := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 2),
a := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 3) } =
f ↑x ↑y | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < (ofFn w h chunk f).width
yh : ↑y < (ofFn w h chunk f).height
⊢ { r := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y),
g := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 1),
b := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 2),
a := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 3) } =
f ↑x ↑y | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < (ofFn w h chunk f).width
⊢ { r := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y),
g := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 1),
b := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 2),
a := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 3) } =
f ↑x ↑y
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | simp only [width_ofFn, height_ofFn, Color.ext_iff] at xw yh ⊢ | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < (ofFn w h chunk f).width
yh : ↑y < (ofFn w h chunk f).height
⊢ { r := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y),
g := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 1),
b := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 2),
a := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 3) } =
f ↑x ↑y | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y) = (f ↑x ↑y).r ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 1) = (f ↑x ↑y).g ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 2) = (f ↑x ↑y).b ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < (ofFn w h chunk f).width
yh : ↑y < (ofFn w h chunk f).height
⊢ { r := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y),
g := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 1),
b := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 2),
a := (ofFn w h chunk f).data.get! (base (ofFn w h chunk f).width (ofFn w h chunk f).height ↑x ↑y + 3) } =
f ↑x ↑y
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | have w0 : 0 < w := by omega | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y) = (f ↑x ↑y).r ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 1) = (f ↑x ↑y).g ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 2) = (f ↑x ↑y).b ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y) = (f ↑x ↑y).r ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 1) = (f ↑x ↑y).g ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 2) = (f ↑x ↑y).b ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y) = (f ↑x ↑y).r ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 1) = (f ↑x ↑y).g ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 2) = (f ↑x ↑y).b ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | have yh' : y ≤ h - 1 := by omega | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y) = (f ↑x ↑y).r ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 1) = (f ↑x ↑y).g ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 2) = (f ↑x ↑y).b ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y) = (f ↑x ↑y).r ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 1) = (f ↑x ↑y).g ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 2) = (f ↑x ↑y).b ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y) = (f ↑x ↑y).r ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 1) = (f ↑x ↑y).g ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 2) = (f ↑x ↑y).b ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | have m0 : ∀ x : Fin 4, (x * 4 : Fin 4) = 0 := by
intro x
have e : (4 : Fin 4) = 0 := rfl
simp only [e, mul_zero] | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y) = (f ↑x ↑y).r ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 1) = (f ↑x ↑y).g ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 2) = (f ↑x ↑y).b ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y) = (f ↑x ↑y).r ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 1) = (f ↑x ↑y).g ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 2) = (f ↑x ↑y).b ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y) = (f ↑x ↑y).r ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 1) = (f ↑x ↑y).g ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 2) = (f ↑x ↑y).b ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | have f0 : 0 < 4 := by norm_num | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y) = (f ↑x ↑y).r ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 1) = (f ↑x ↑y).g ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 2) = (f ↑x ↑y).b ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y) = (f ↑x ↑y).r ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 1) = (f ↑x ↑y).g ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 2) = (f ↑x ↑y).b ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y) = (f ↑x ↑y).r ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 1) = (f ↑x ↑y).g ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 2) = (f ↑x ↑y).b ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | refine ⟨?_, ?_, ?_, ?_⟩ | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y) = (f ↑x ↑y).r ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 1) = (f ↑x ↑y).g ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 2) = (f ↑x ↑y).b ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a | case refine_1
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y) = (f ↑x ↑y).r
case refine_2
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y + 1) = (f ↑x ↑y).g
case refine_3
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y + 2) = (f ↑x ↑y).b
case refine_4
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y) = (f ↑x ↑y).r ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 1) = (f ↑x ↑y).g ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 2) = (f ↑x ↑y).b ∧
(ofFn w h chunk f).data.get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | omega | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
⊢ 0 < w | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
⊢ 0 < w
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | omega | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
⊢ ↑y ≤ h - 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
⊢ ↑y ≤ h - 1
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | intro x | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
⊢ ∀ (x : Fin 4), x * 4 = 0 | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x✝ : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x✝ < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
x : Fin 4
⊢ x * 4 = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
⊢ ∀ (x : Fin 4), x * 4 = 0
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | have e : (4 : Fin 4) = 0 := rfl | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x✝ : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x✝ < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
x : Fin 4
⊢ x * 4 = 0 | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x✝ : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x✝ < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
x : Fin 4
e : 4 = 0
⊢ x * 4 = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x✝ : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x✝ < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
x : Fin 4
⊢ x * 4 = 0
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | simp only [e, mul_zero] | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x✝ : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x✝ < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
x : Fin 4
e : 4 = 0
⊢ x * 4 = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x✝ : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x✝ < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
x : Fin 4
e : 4 = 0
⊢ x * 4 = 0
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | norm_num | f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
⊢ 0 < 4 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
⊢ 0 < 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | nth_rw 1 [ofFn] | case refine_4
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a | case refine_4
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ { data := parallel_colors (fun i => f (i % w) (h - 1 - i / w)) (h * w) chunk, width := w, height := h,
size_eq := ⋯ }.data.get!
(base w h ↑x ↑y + 3) =
(f ↑x ↑y).a | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_4
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ (ofFn w h chunk f).data.get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | simp only | case refine_4
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ { data := parallel_colors (fun i => f (i % w) (h - 1 - i / w)) (h * w) chunk, width := w, height := h,
size_eq := ⋯ }.data.get!
(base w h ↑x ↑y + 3) =
(f ↑x ↑y).a | case refine_4
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ (parallel_colors (fun i => f (i % w) (h - 1 - i / w)) (h * w) chunk).get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_4
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ { data := parallel_colors (fun i => f (i % w) (h - 1 - i / w)) (h * w) chunk, width := w, height := h,
size_eq := ⋯ }.data.get!
(base w h ↑x ↑y + 3) =
(f ↑x ↑y).a
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | rw [get!_parallel_colors] | case refine_4
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ (parallel_colors (fun i => f (i % w) (h - 1 - i / w)) (h * w) chunk).get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a | case refine_4
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ (f ((base w h ↑x ↑y + 3) / 4 % w) (h - 1 - (base w h ↑x ↑y + 3) / 4 / w))[↑(base w h ↑x ↑y + 3)] = (f ↑x ↑y).a
case refine_4.lt
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ base w h ↑x ↑y + 3 < h * w * 4 | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_4
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ (parallel_colors (fun i => f (i % w) (h - 1 - i / w)) (h * w) chunk).get! (base w h ↑x ↑y + 3) = (f ↑x ↑y).a
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | simp [base, add_comm _ (x : ℕ), Nat.add_mul_div_right _ _ w0, Nat.div_eq_of_lt xw,
Nat.sub_sub_self yh', Nat.mod_eq_of_lt xw, m0, add_comm (_ * 4),
Nat.add_mul_div_right _ _ f0] | case refine_4
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ (f ((base w h ↑x ↑y + 3) / 4 % w) (h - 1 - (base w h ↑x ↑y + 3) / 4 / w))[↑(base w h ↑x ↑y + 3)] = (f ↑x ↑y).a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_4
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ (f ((base w h ↑x ↑y + 3) / 4 % w) (h - 1 - (base w h ↑x ↑y + 3) / 4 / w))[↑(base w h ↑x ↑y + 3)] = (f ↑x ↑y).a
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | have le := base_le xw yh | case refine_4.lt
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ base w h ↑x ↑y + 3 < h * w * 4 | case refine_4.lt
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
le : base w h ↑x ↑y + 4 ≤ h * w * 4
⊢ base w h ↑x ↑y + 3 < h * w * 4 | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_4.lt
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
⊢ base w h ↑x ↑y + 3 < h * w * 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Image.lean | Image.get_ofFn | [209, 1] | [233, 14] | omega | case refine_4.lt
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
le : base w h ↑x ↑y + 4 ≤ h * w * 4
⊢ base w h ↑x ↑y + 3 < h * w * 4 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_4.lt
f : ℕ → ℕ → Color UInt8
w h chunk : ℕ
x : Fin (ofFn w h chunk f).width
y : Fin (ofFn w h chunk f).height
xw : ↑x < w
yh : ↑y < h
w0 : 0 < w
yh' : ↑y ≤ h - 1
m0 : ∀ (x : Fin 4), x * 4 = 0
f0 : 0 < 4
le : base w h ↑x ↑y + 4 ≤ h * w * 4
⊢ base w h ↑x ↑y + 3 < h * w * 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_pos_lt_sq | [15, 1] | [15, 55] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
h : 0 < x
⊢ x ^ 2 > 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
h : 0 < x
⊢ x ^ 2 > 0
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_pos_gt_sq | [16, 1] | [16, 55] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
h : x > 0
⊢ x ^ 2 > 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
h : x > 0
⊢ x ^ 2 > 0
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_pos_mul | [17, 1] | [17, 67] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
p : x > 0
q : y > 0
⊢ x * y > 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
p : x > 0
q : y > 0
⊢ x * y > 0
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_pos_div | [18, 1] | [18, 67] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
p : x > 0
q : y > 0
⊢ x / y > 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
p : x > 0
q : y > 0
⊢ x / y > 0
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_pos_4 | [19, 1] | [19, 37] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 < 4 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 < 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_pos_7 | [20, 1] | [20, 37] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 < 7 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 < 7
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_pos_4_real | [21, 1] | [21, 48] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 < 4 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 < 4
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_pos_7_real | [22, 1] | [22, 48] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 < 7 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 < 7
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_pos_zero_one | [23, 1] | [23, 50] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 < 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 < 1
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_pos_nnreal | [24, 1] | [24, 60] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
h : u > 0
⊢ 0 < ↑u | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
h : u > 0
⊢ 0 < ↑u
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_pos_pow | [25, 1] | [25, 41] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 < 2 ^ n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 < 2 ^ n
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_pos_inv | [26, 1] | [26, 47] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 < 1⁻¹ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 < 1⁻¹
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_abs | [34, 1] | [34, 39] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 ≤ Complex.abs z | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 ≤ Complex.abs z
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_abs_ge | [35, 1] | [35, 42] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ Complex.abs z ≥ 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ Complex.abs z ≥ 0
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_nn_sq | [36, 1] | [36, 39] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ x ^ 2 ≥ 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ x ^ 2 ≥ 0
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_mul | [37, 1] | [37, 63] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
p : x ≥ 0
q : y ≥ 0
⊢ x * y ≥ 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
p : x ≥ 0
q : y ≥ 0
⊢ x * y ≥ 0
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_div | [38, 1] | [38, 63] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
p : x ≥ 0
q : y ≥ 0
⊢ x / y ≥ 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
p : x ≥ 0
q : y ≥ 0
⊢ x / y ≥ 0
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_add | [39, 1] | [39, 63] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
p : x ≥ 0
q : y ≥ 0
⊢ x + y ≥ 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
p : x ≥ 0
q : y ≥ 0
⊢ x + y ≥ 0
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_nat | [40, 1] | [40, 41] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ ↑n ≥ 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ ↑n ≥ 0
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_num | [41, 1] | [41, 35] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 ≤ 7 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 ≤ 7
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_num_real | [42, 1] | [42, 46] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 ≤ 7 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 ≤ 7
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_zero_one | [43, 1] | [43, 46] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 ≤ 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 ≤ 1
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_nnreal | [44, 1] | [44, 44] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 ≤ ↑u | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 ≤ ↑u
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_zero | [45, 1] | [45, 42] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 ≤ 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 ≤ 0
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_pow | [46, 1] | [46, 37] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 ≤ 2 ^ n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 ≤ 2 ^ n
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_inv | [47, 1] | [47, 43] | bound | n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 ≤ 0⁻¹ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x y : ℝ
u : ℝ≥0
z : ℂ
⊢ 0 ≤ 0⁻¹
TACTIC:
|
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